Answer:
Step-by-step explanation:
The easiest way to do this is to clear the decimal by multiplying the numerator and the denominator by
10
.
You can reduce the fraction later.
40
m
48
m
2) Reduce the fraction to its simplest form
Cancel out
8
from the top and the bottom
5
m
6
m
←
answer
This answer means that the numerator and denominator of the given fraction
4
m
4.8
m
are in a
5
:
6
ratio relationship with each other.
Check
Is
4
4.8
equal to
5
6
?
Cross multiply
(
4
)
(
6
)
should be equal to
(
5
)
(
4.8
)
24
is equal to
24.0
C
h
e
c
k
A line has a slope of 8 and includes the points (9, u) and (10, –1). What is the value of u?
Answer: -9
Step-by-step explanation: To find the value of u, we can use the slope formula to calculate the slope of the line that goes through the points (9, u) and (10, -1). The slope formula is: slope = (y2 - y1)/(x2 - x1). In this case, we have: slope = (-1 - u)/(10 - 9) = (-1 - u)/1. Since the slope of the line is given as 8, we can set this equal to the value we calculated above and solve for u. This gives us: 8 = (-1 - u)/1. Multiplying both sides by 1 gives us: 8 = -1 - u. Adding 1 to both sides gives us: 9 = -u. Finally, negating both sides gives us: u = -9. Therefore, the value of u is -9.
john drove for 3 hours at a rate of 50 miles per hour and for 2 hours at 60 miles per hour. what was his average speed for the whole journey?
The average speed is 54 miles per hour.
What is average ?
In plain English, an average is one number chosen to represent a list of numbers. It is often calculated by dividing the total number of numbers in the list by the number of numbers in the list. As an illustration, the sum of the integers 2, 3, 4, 7, and 9 is 5.
The definition of the average is the mean value, which is the ratio of the sum of the values in a given set to the total number of values in the set.
The formula for distance is
Distance = Rate × Time
Total distance = 50 × 3 + 60 × 2 = 270
Total time = 3 + 2 = 5
Using the formula:
[tex]Speed = \frac{Distance}{Time}[/tex]
= 270 / 5
= 54
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A study obtained data on the amount of time 32 randomly selected young adults spent on their cell phones pre-pandemic and then during the lockdown phase of the pandemic. The investigator is interested in determining whether there is evidence that the amount of time young adults spent on their cell phone during the lockdown increased when compared to pre-pandemic times. Let
L=
time spent on phone during lockdown;
P=
time spent on phone prepandemic time; and
d=L−P
Question 4 (1 point) The data are paired because: The conclusion pertains to a mean difference. All of these are true Each element in the sample is measured twice: once pre-pandemic and once in lockdown There is only one sample
The Null hypothesis and alternative hypothesis for the given sample of cell phone spent time data of 32 randomly selected adults during lockdown and pre-pandemic times are,
H₀ : μd = 0 and Hₐ : μd > 0
Correct option is option (d).
What is hypothesis testing?
To decide whether a hypothesis should be accepted or rejected, statisticians utilize formal, planned procedures known as hypothesis testing. Hypothesis testing is the process of choosing hypotheses for a specific probability distribution based on observable evidence.
Given:
A study obtained time data of 32 randomly selected young adults spent on their cell phones pre-pandemic and then during the lockdown phase of the pandemic. let us consider,
L --> time spent on cell phone by adults during lockdown
P --> time spent on cell phone by adults at pre pandemic time
and d = L- P
we want to perform a hypothesis testing on this sample .
The samples are dependent because same adults are being sampled before and after the lockdown.
Also, we need to test if mean time after is higher than mean time before so this is a right tailed test. Hence,
The correct hypotheses will be:
H₀ : μd= 0
Hₐ : μd> 0
Hence, option D is the correct option.
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Given the least-squares regression line, In(Element) = 2.305 -0.101(Time), what is the predicted amount of an
unstable element that is left after 6 years?
and explanation
The predicted amount of an unstable element that is left after 6 years is 5.46 grams.
Explain the least-squares regression line?A least-squares regression line, that minimizes the vertical distance between the data points and the regression line, is the line that best fits a linear relation between two variables when the data indicates such a relationship.For the stated question-
The equation for the least-squares regression line, is;
In(Element) = 2.305 -0.101(Time)
Amount of unstable element left after time t = 6 years.
In (Element) = 2.305 -0.101(6)
ln (Element) = 1.699
(Element) = e¹°⁶⁹⁹
(Element) = 5.46
Thus, the predicted amount of an unstable element that is left after 6 years is 5.46 grams.
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rewrite x+6=0 in slope intercept form
Answer:x=6
Step-by-step explanation:You can simplify as 0 is worh nothing so it would be just 6
The perimeter of a square is equal to the perimeter of an equilateral triangle. the length of a side of the square is given by x, and the length of a side of the equilateral triangle is given by x 1. which equation can be used to find the value of x? x = 3 (x 1) 3 x = 4 (x 1) 4 x = 3 (x 1) x = x 1
The equation used to determine the value of x for the length of a square side is: 4 x = 3 (x 1).
Explain the term equilateral triangle?An equilateral triangle, which is frequently referred to as a "regular" triangle, is a triangle with three equal-length sides. Because all three sides of an isosceles triangle are equal, an equilateral triangle is a particular case of just an isosceles triangle.The given condition are-
A square's perimeter is the same as an equilateral triangle's perimeter.x determines the length of a square side, while x1 determines the length of an equilateral triangle side.Perimeter of square = 4x
Equilateral triangle perimeter = 3(x 1)
Equating both by the condition-
4x = 3(x 1)
Thus, the equation used to determine the value of x for the length of a square side is: 4 x = 3 (x 1).
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Find the equation that represents the proportional relationship in this graph, for y in terms of x.
The equation that represents the proportional relationship in this graph is y = 2 / 7 x.
How to find proportional relationship?Two variables have a proportional relationship if all the ratios of the variables are equivalent.
A proportional relationship is one in which two quantities vary directly with each other.
We say the variable y varies directly as x if:
y = kxfor some constant k , called the constant of proportionality .
Therefore, the variables in this case are y and x.
Hence, let's find k using the coordinates on the graph
(0.7, 0.2)
0.2 = k (0.7)
k = 0.2 / 0.7
k = 2 / 7
Hence,
y = 2 / 7 x
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A gas station is open 365 day a year, 24 hours a day. The store owner estimates that they served 40,000 cups of coffee last year. This quantity can also be expressed as
functions
equation editor
cups of coffee per hour (round to the nearest whole cup). This is a ? reasonable not reasonable estimate.
A gas station is open 365 day a year, 24 hours a day. If the gas station served 40,000 cups of coffee last year, then it served an average of 5 cups of coffee per hour.
The problem can be solved using the average value approach.
Average value = total amount or sum of data / number of data
In the given problem,
total amount = total coffee served last year
total amount = 40,000
number of data = number of hours in a year
number of data = 365 day/year x 24 hours/day = 8760 hours
Hence,
Average value = total amount or sum of data / number of data
= 40000 / 8760
= 4,6 ≈ 5 (round to the nearest whole cup)
Hence, the average coffee served is 5 cups per hour.
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Find the slope of the line going through the points (2,4) and (12)
Step-by-step explanation:
If there are 2 points (a,b) and (c,d),
then the slope = (d - b)/(c - a) = (b - d)/(a - c)
Therefore slope = (10 - 4)/(4 - 2) = 6/2 = 3
The point-slope form of a line is
y = mx + b, where m is the slope and b is the y-intercept Substituting either point (2,4) or (4,10) into the equation is fine.
(4) = (3)(2) + b
4 = 6 + b
b = 4 - 6 = -2
y = 3x - 2
Or
(10)=(3)(4) + b
10 = 12 + b
b = 10 - 12 = -2
y = 3x - 2
3. Gina was working in the laboratory on an experiment involving the population of bacteria. If her initial starting amount in a petri dish was 125 bacteria, how many would be in the petri dish after 24 hours? Show your work
The number of bacteria in the petri dish after 24 hours will be y = 125 + 24x
What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.Given is Gina was working in the laboratory on an experiment involving the population of bacteria. Her initial starting amount in a petri dish was 125 bacteria.
Assume that each hour the bacteria rises by [x] bacteria per hour. Then,
the number of bacteria in the petri dish after 24 hours will be -
y = 125 + 24x
Therefore, the number of bacteria in the petri dish after 24 hours will be y = 125 + 24x.
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Anyone willing to help
Answer:
x3=5x+e3x+2−17
This is the best I can do :D
Helpppppppppp meeeeee
Answer:
1.07 maybe... don't trust me on that
Answer:
x = -6
Step-by-step explanation:
The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle.
We can write the following equation based on this information to calculate value of x:
64 + 27 = 97 + x
Add like terms91 = 97 + x
subtract 97 from both sides91 - 97 = 97 - 97 + x
-97 will eliminate the 97 on the right side of the equation-6 = x
what is the simplified product of 2/5+2/3
[tex] \frac{2}{5} + \frac{2}{3} = \\ lcm \: of \: 5 \: and \: 3 \: is \: 15 \: so \\ \frac{6 + 10}{15} = = \: \frac{16}{15} [/tex]
Therefore, the answer is
[tex]{ \red{ \sf{ \frac{16}{5}}}}[/tex]
[tex]\colorbox{pink}{\blue{ \boxed{ \tt{ hope \: it \: helps \: you}}}}[/tex]
Step-by-step explanation:
[tex]{ \blue{ \sf{ \frac{2}{5} + \frac{2}{3}}}}[/tex]
If you take the Lowest Common Multiple (L.C.M.) you will get 15.
[tex]{ \blue{ \sf{ \frac{6+10}{15}}}}[/tex]
[tex]{= \blue{ \sf{ \frac{16}{15}}}}[/tex]
Which of the following has the same value as -5 - 15?
A -15 - (-5)
B-5 + 15
C-5 + (-15)
D-15 + 5
Answer:
C -5 + (-15)
Step-by-step explanation:
-5 - 15 = -20
A -15 - (-5) = -15 + 5 = -10
B -5 + 15 = 10
C -5 + (-15) = -20
D -15 + 5 = -10
Answer:
c; -5+(-15)
Step-by-step explanation:
-5-15=-20
adding a negative number is subtraction, which means;
-5+(-15)=-20
therefore
-5-15=-20=-5+(-15)
If you bought a stock last year for a price of $79, and it has gone down 8.7% since then, how much is the stock worth now, to the nearest cent?
Answer:
72.13
Step-by-step explanation:
If you bought a stock last year for a price of $79, and it has gone down 8.7% since then, how much is the stock worth now, to the nearest cent?
The table shows the last holiday destination of 60 people.Holiday
destinations
Frequency | Angle in º
France
25
Spain
18
Greece
15
Other
2
Complete the table and draw a pie chart
to represent this information.
Note: Please draw your pie chart in a 'clockwise' direction from the line already drawn
and follow the order from the table (France, then Spain etc...).
The required answer are according to the following order,
a) France;
25/60 × 360/1 = 150°
b) Spain;
18/60 × 360/1 = 108°
c) Greece;
15/60 × 360/1 = 90°
d) Other;
2/60 × 360/1 = 12°
What do you mean by sum of angles?
We know that the sum of angles in a triangle is 360°. The question requires us to find the angle that corresponds to each of the given holiday destinations. We shall now proceed as follows:
The angle subtended is obtained from number of people that chose a particular location.
a) France;
25/60 × 360/1 = 150°
b) Spain;
18/60 × 360/1 = 108°
c) Greece;
15/60 × 360/1 = 90°
d) Other;
2/60 × 360/1 = 12°
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The ______________ function is used to compute the number of times a particular condition is satisfied within a given range of cells.
The COUNTIF function is used to compute the number of times a particular condition is satisfied within a given range of cells.
What is countif?It is an excel statistical function, which is used to count the number of cells that meet a criterion. To determine how many cells in the worksheet contain a number higher than or less than the one specified, the countif formula is used.
It is typed =COUNTIF
Steps to use the =COUNTIF function:1. Select a cell
2. Type =COUNTIF
3. Double-click the COUNTIF command
4. Select a range
5. Type
,6. Select a cell (the criteria, the value that you want to count)7.
Hit enter Hence the answer is COUNTIF
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A set of shirt prices are normally distributed with a mean of 454545 dollars and a standard deviation of 555 dollars. What proportion of shirt prices are between 373737 dollars and 59. 3559. 3559, point, 35 dollars?.
The total proportion of shirts between two prices is 0.9431, which is obtained using the knowledge of proportion and statistics.
What is proportion?
In mathematics, a proportion is defined as the comparison between two numerical quantities. If both possess the same nature, they are called directly proportional, or else called inversely proportional.
Calculation of the proportion based on the problem
The mean and standard deviation are given to be 45 and 5 respectively
Calculate standard normal variate using the formula, z = (x - 45) / 5
Taking x = 37, we get,
z1 = (37 - 45) / 5
= -1.6
Using the z table, we get the value, z1 = 0.0548
Now, taking x = 59.35, we get,
z2 = (59.35 - 45) / 5
= 2.87
Using the z table, we get the value, z2 = 0.9979
The proportion between two prices is given by z = z2 - z1
z = 0.9979 - 0.0548
= 0.9431
Hence, the proportion of shirts between the two prices is 0.9431.
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What percent of 60 is 51?
Answer:
85%
Step-by-step explanation:
Hope it helps!
Answer:
85%
Step-by-step explanation:
51/60=.85=85%
The bag contained red marbles and blue marbles.red marbles to blue marbles was 5 to 3 what fraction of the marbles were blue
Answer:
53
Step-by-step explanation:
Solve for h:
2h-4x=-6y
Please provide steps also
Answer:
h = -3y + 2x
Step-by-step explanation:
Add 4x to both sides of the equation.
2h = −6y + 4x
Divide each term in 2h = −6y + 4x by 2 and simplify.
Divide each term in 2h = −6y + 4x by 2.
2h/2 = -6y/2 + 4x/2
Simplify the left side.
h = −6y/2 + 4x/2
Simplify the right side.
Simplify each term.
Cancel the common factor of −6 and 2.
h = -3y+2(2x)/2
Cancel the common factors.
Factor 2 out of 2.
h = -3y+2(2x)/2(1)
Cancel the common factor
h = -3y+2(2x)/2(1)
Rewrite the expression
h = -3y + 2x/1
Divide 2x by 1.
h = -3y + 2x
hopefully its right LOLZ
Amber is given a Stanford-Binet intelligence test. Her mental age is determined to be 14, and her chronological age is 10. Which of the following is true of Amber? A) Her IQ score is 86. B) Her IQ score is about average. C) Her IQ score is below the majority of the population. D) Her IQ score is above the majority of the population types of intelligence.
The correct option is . D) Her IQ score is above the majority of the population types of intelligence.
IQ is an abbreviation for intelligence quotient. IQ tests are used to assess people's intellectual abilities and potential. They are intended to test a wide range of cognitive abilities, including reasoning, logic, and problem-solving.
It's a test of intelligence, which you're born with. It is not a test of knowledge that represents what you learn in school or through life experience.
Amber's mental age = 14
Amer's age = 10
Then her IQ can be calculated by
[tex]IQ=\frac{mental\ age}{chronological\ age}*100=\frac{14}{10}*100=140[/tex]
Average IQ of majority of population is between 85 to 115.
Only small percentage of population has IQ score higher than 130.
It means Amber's IQ score is above the majority of the population.
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x:2 + 8 =-24[tex]x/2 + 8 =-24.which step should sammy complete first
The step which Sammy should complete first in a bid to solve the equation is; subtraction 8 from both sides of the equation.
Which step should Sammy complete first to solve the equation?It follows from the task content that the step which Sammy should complete first in a bid to solve the equation.
Since the given equation is;
x/2 + 8 = -24
Therefore, in a bid to solve the equation; the first step which Sammy must complete first in a bid to solve the equation is;
Subtract 8 from both sides of the equation; so that we have;
x/2 = -24 -8
x/2 = -32
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[tex]2x^2-4x+3=0[/tex]
Solve the quadratic equation using the quadratic formula or completing the square. Show exact answers in simplified, radical form; no rounded decimals.
**Show steps
The solution to the quadratic equation using quadratic formula is X has a negative value x is undefined with no real solution.
x= [tex]\frac{4 + 3.41i}{4}[/tex] or x= [tex]\frac{4 - 3.14i}{4}[/tex]
Using quadratic formula to solve the equation
[tex]x = \frac{-b +or - \sqrt{b^{2}-4ac } }{2a}[/tex]
2x^2-4x +3 = 0
All equations of the form ax^2+bx+c=0 can be solved using the quadratic formula:
The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
we need to identify a, b and c
from the quadratic equation a = 2, b= -4 and c=3
[tex]x = \frac{-b +or - \sqrt{b^{2}-4ac } }{2a}[/tex]
Substitute the value of a, b and c into the equation
[tex]x = \frac{-(-4) ± \sqrt{(-4^{2} - 4(2)(3)} }{2(2)}[/tex]
[tex]x=\frac{ 4 ± \sqrt{16 -28} }{4}[/tex]
x= [tex]\frac{4+\sqrt{-12} }{4}[/tex] or x= [tex]\frac{4-\sqrt{-12} }{4}[/tex]
x= [tex]\frac{4 + 3.41i}{4}[/tex] or x= [tex]\frac{4 - 3.14i}{4}[/tex]
Since X has a negative value x is undefined with no real solution.
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Answer:
[tex]x=\dfrac{2+\sqrt{2}\: i}{2}, \quad x=\dfrac{2-\sqrt{2}\: i}{2}[/tex]
Step-by-step explanation:
Given quadratic equation:
[tex]2x^2-4x+3=0[/tex]
When completing the square for a quadratic equation in the form ax²+bx+c=0, first move the constant to the right side of the equation:
[tex]2x^2-4x=-3[/tex]
Divide both sides of the equation by the coefficient of x²:
[tex]x^2-2x=-\dfrac{3}{2}[/tex]
Add the square of half the coefficient of the term in x to both sides to form a perfect square trinomial on the left side:
[tex]x^2-2x+\left(\dfrac{-2}{2}\right)^2=-\dfrac{3}{2}+\left(\dfrac{-2}{2}\right)^2[/tex]
Simplify:
[tex]x^2-2x+1=-\dfrac{3}{2}+1[/tex]
[tex]x^2-2x+1=-\dfrac{1}{2}[/tex]
Factor the perfect square trinomial on the left side:
[tex](x-1)^2=-\dfrac{1}{2}[/tex]
Square root both sides:
[tex]\sqrt{(x-1)^2}=\sqrt{-\dfrac{1}{2}}[/tex]
[tex]x-1=\pm\sqrt{-\dfrac{1}{2}}[/tex]
Simplify:
[tex]x-1=\pm\sqrt{\dfrac{1}{2} \cdot -1}[/tex]
[tex]x-1=\pm\sqrt{\dfrac{1}{2}} \sqrt{-1}[/tex]
[tex]x-1=\pm\dfrac{1}{\sqrt{2}} i[/tex]
[tex]x-1=\pm\dfrac{\sqrt{2}}{2} i[/tex]
Add 1 to both sides:
[tex]x=1\pm\dfrac{\sqrt{2}}{2} i[/tex]
[tex]x=\dfrac{2}{2}\pm\dfrac{\sqrt{2}}{2} i[/tex]
[tex]x=\dfrac{2\pm\sqrt{2}\: i}{2}[/tex]
Therefore, the solutions of the given quadratic equation using the method of completing the square are:
[tex]x=\dfrac{2+\sqrt{2}\: i}{2}, \quad x=\dfrac{2-\sqrt{2}\: i}{2}[/tex]
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(c) a farm brings 11 tons of watermelon to market. find a 92% confidence interval for the population mean cash value of this crop. what is the margin of error? hint: 1 ton is 2000 pounds. (round your answers to the nearest dollar.)
The farm's 11 tons of watermelon will have a 92% confidence interval mean cash value of $148.89, which is within the margin of error.
What is margin of error?In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings. Simply said, you may determine the degree of unpredictability in data and study results using the margin of error. Your findings will vary from the actual population figure by how many percentage points, as shown by the margin of error. A 95% confidence interval with a 4% margin of error, for instance, indicates that your statistic will, 95% of the time, be within 4% of the true population figure.
Here,
n = 38
x = 6.88
= 1.86
= 1-.90
= .10
/2 = .05
z(/2) = -1.64
-z(/2) = 1.64
P(-1.645 < z < 1.645) = .90
Margin of error= z(/2)(/√n)
= 1.645(1.86/√38)
= $.4963(300)
= $148.89
The margin of error for a farm brings 11 tons of watermelon to market with 92% confidence interval for the population mean cash value of this crop will be $148.89.
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write a congruence statement for the polygons. identify all pairs of congruent corresponding parts
Please help. problem #1
The polygon ABCD and polygon EFGH are congruent polygons.
What is a polygon?A polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,
Examples of polygons, equilateral triangles, squares, pentagons, etc
Here,
Consider two polygons,
ABCD and EFGH,
As given in the figure,
AB = EF,
AD = EH
∠A = ∠E
∠D = ∠H
ABCD ≅ EFGH,
Thus, Congruent polygons are polygons ABCD and EFGH.
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a research engineer for a tire manufacturer is investigating tire life for a new rubber compound and has built 16 tires and tested them to end-of-life in a road test. the sample mean and standard deviation are 60,139.7 and 3517.57 kilometers. can you conclude, using ????
There is no sufficient evidence to indicate the true standard deviation is less than 4000
What is standard deviation ?
The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.
given that n = 16
x = 60139.7
s = 3718.06
∝ = 0.05
To test the hypothesis
H0 : = 4000
H1 : < 4000 (claim)
test statistics
x² = ((n-1)s²) / H0²
= (15 * 13823970.16) / (16000000)
= 12.96
P- value = P [x² < 12.96] DF = n-1 = 15
= 0.3946
0.1 < P-value <0.5
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A pentagon is made up of an equilateral △ABC of side length 2cm on top of a square BCDE. Circumscribe a circle through points, A,D and E. The radius of the circle isA1+√32B5−2√3C 2D 1+√3
An equilateral △ABC with a side length of 2 cm is placed on top of a square BCDE to form a pentagon. A circle is drawn including points A, D, and E. And the radius of this circle is found to be 2 cm.
A triangle is said to be equilateral if all three of its sides are the same length and each of its three angles measures 60 degrees.
The given triangle is equilateral with a side length of 2cm. This triangle is on the top of a square BCDE. The circle circumscribes through the A, D, and E of the given shapes.
Using the given details, first, draw the diagram. Let H is the circumcenter of ADE. In the diagram, draw the altitude of AG passing through the circumcenter and square as GF.
From the diagram, let GH be x. The side of the triangle is 2 cm and the altitude cut it into two equal halves. Then, BG=EF=1 cm, HF=2-x, and HE=x+√3
[tex]\begin{aligned}\sin \theta &= \frac{AG}{AB}\\\sin 60^{\textdegree} &=\frac{AG}{2}\\\frac{\sqrt{3}}{2}&=\frac{AG}{2}\\AG&=\sqrt{3}\end{aligned}[/tex]
By Pythagoras' theorem, from ΔHEF,
[tex]\begin{aligned}HE^{2}&=HF^{2}+EF^{2}\\\left(x+\sqrt{3}\right)^2&=(2-x)^2+1^2\\x^2+3+2\sqrt{3}x&=4-4x+x^2+1\\(4+2\sqrt{3})x&=5-2\\x&=\frac{2}{4+2\sqrt{3}}\\&=\frac{2}{2(2+\sqrt{3})}\times\frac{2-\sqrt{3}}{2-\sqrt{3}}\\&=\frac{2-\sqrt{3}}{4-3}\\&=2-\sqrt{3}\end{alinged}[/tex]
The radius of the circle (HE) is 2-√3+√3=2.
The answer is 2 cm. Therefore, option C is correct.
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translate each of the following multiplicative expressions into its additive counterpart. assume that the operation is commutative. a. a2b3 b. a22(b21c)2 c. (ab2)23c2 5 e
The additive counterpart of given expressions are (2a+3b), -2a+2(-b+c), and -3(a+2b)+2c=0.
When two numbers may be added together or multiplied, regardless of the order in which they are entered, the result is said to be commutative. There are different formulas available for the conversion of multiplicative expressions to their additive counterparts.
a) The first expression is a²b³. This expression is written as aabbb. This is of the form ab and its corresponding additive counterpart is of the form a+b.
Then, a+a+b+b+b=2a+3b.
b) The second expression is a⁻²(b⁻¹c)². This expression is of the form a⁻¹ and its corresponding additive counterpart is of the form -a.
Then,
[tex]\begin{aligned}a^{-2}(b^{-1}c)^2&=a^{-1}a^{-1}(b^{-1}c)(b^{-1}c)\\&=-a-a-b+c-b+c\\&=-2a+2(-b+c)\end{aligned}[/tex]
c) The third expression is (ab²)⁻³c²=e. This expression is first expanded as, (ab²)⁻¹(ab²)⁻¹(ab²)⁻¹c²=e. Using property, (xy)⁻¹=y⁻¹x⁻¹.
Then,
[tex]\begin{aligned}((b^2)^{-1}a^{-1})((b^2)^{-1}a^{-1})((b^2)^{-1}a^{-1})c^2&=e\\(b^{-2}a^{-1})(b^{-2}a^{-1})(b^{-2}a^{-1})c^2&=e\end{aligned}[/tex]
Also, the additive identity to e is zero. And, aⁿ=na.
Then,
(-2b-a)+(-2b-a)+(-2b-a)+2c=0
Simplifying we get,
-3(a+2b)+2c=0.
The answers are (2a+3b), -2a+2(-b+c), and -3(a+2b)+2c=0.
The complete question is -
Translate each of the following multiplicative expressions into its additive counterpart. assume that the operation is commutative
a. a²b³
b. a⁻²(b⁻¹c)²
c. (ab²)⁻³c²=e
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What percent
↓
of 60 is 51?
↓ ↓ ↓
X 60 = 51
Answer:85%
Step-by-step explanation:
51 is what percent of 60 is equal to (51 / 60) x 100 = 85%. So if you buy an item at $60 with $51 discounts, you will pay $9 and get 85% discount cashback rewards. So 51 out of 60 as a percentage is 85%